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# NCERT Solutions for Class 8 Maths Chapter 6 - Cubes and Cube Roots Exercise 6.2

Last updated date: 06th Sep 2024
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## NCERT Solutions for Maths Exercise 6.2 Class 8 Chapter 6 Cubes and Cube Roots - FREE PDF Download

Class 8 Maths Ch 6 Ex 6.2 focuses on the concepts of cubes and cube roots. This exercise is designed to help students understand how to find the cube of a number and determine the cube root of given values. These concepts are essential for building a strong foundation in mathematics, as they are used in various advanced topics. The key to mastering this exercise is to pay attention to the properties of cubes and cube roots. Students should focus on learning the rules and methods for calculating these values accurately. By practising the problems in class 8 maths 6.2, students will enhance their problem-solving skills and gain confidence in handling more complex mathematical tasks. Class 8 maths 6.2 serves as a crucial step in preparing for higher-level maths studies. NCERT Solutions for Class 8 Maths Cubes and Cube Roots Exercise 6.2 provides a strong base to tackle exercises confidently and accurately.

Table of Content
1. NCERT Solutions for Maths Exercise 6.2 Class 8 Chapter 6 Cubes and Cube Roots - FREE PDF Download
2. Glance on NCERT Solutions Maths Chapter 6 Exercise 6.2 Class 8 | Vedantu
3. Access NCERT Solutions for Maths Class 8 Chapter 6 Cubes and Cube Roots
4. Class 8 Maths Chapter 6: Exercises Breakdown
5. CBSE Class 8 Maths Chapter 6 Other Study Materials
6. Chapter-Specific NCERT Solutions for Class 8 Maths
FAQs

## Glance on NCERT Solutions Maths Chapter 6 Exercise 6.2 Class 8 | Vedantu

• Chapter 6 of Class 8 Maths focuses on cubes and cube roots. This chapter explores how to find the cube of a number and its cube root using various properties and formulas.

• A Cube of a number 𝑛 is obtained when the number is multiplied by itself three times.

• Finding the Cube Roots  of a number using prime factorization involves breaking down the number into its prime factors and then grouping these factors to determine the Cube Root.

• It emphasizes understanding the relationships between numbers, which is fundamental for more advanced mathematical concepts.

• There are two questions in Exercise 6.2 Cubes and Cube Roots Class 8 which are fully solved by experts at Vedantu.

## Access NCERT Solutions for Maths Class 8 Chapter 6 Cubes and Cube Roots

### Exercise 6.2

1. Find the cube root of each of the following numbers by prime factorisation method

i. $64$

Ans: Expand $64$ in factors of prime numbers.

$64 = 2 \times 2 \times 2 \times 2 \times 2 \times 2$

$= {2^3} \times {2^3}$

Take cube root on both sides of equation.

$\because 64 = {2^3} \times {2^3}$

$\therefore \sqrt[3]{{64}} = 2 \times 2 = 4$

The cube root of $64$ is $4.$

ii. $512$

Ans: Expand $512$ in factors of prime numbers.

$512 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2$

$= {2^3} \times {2^3} \times {2^3}$

Take cube root on both sides of equation.

$\because 512 = {2^3} \times {2^3} \times {2^3}$

$\therefore \sqrt[3]{{512}} = 2 \times 2 \times 2 = 8$

The cube root of $512$ is $8.$

iii. $10648$

Ans: Expand $10648$ in factors of prime numbers.

$10648 = 2 \times 2 \times 2 \times 11 \times 11 \times 11$

$= {2^3} \times {11^3}$

Take cube root on both sides of equation.

$\because 10648 = {2^3} \times {11^3}$

$\therefore \sqrt[3]{{10648}} = 2 \times 11 = 22$

The cube root of $10648$ is $22.$

iv. $27000$

Ans: Expand $27000$ in factors of prime numbers.

$27000 = 2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 5 \times 5 \times 5$

$= {2^3} \times {3^3} \times {5^3}$

Take cube root on both sides of equation.

$\because 27000 = {2^3} \times {3^3} \times {5^3}$

$\therefore \sqrt[3]{{27000}} = 2 \times 3 \times 5 = 30$

The cube root of $27000$ is $30.$

v. $15625$

Ans: Expand $15625$ in factors of prime numbers.

$15625 = 5 \times 5 \times 5 \times 5 \times 5 \times 5$

$= {5^3} \times {5^3}$

Take cube root on both sides of equation.

$\because 15625 = {5^3} \times {5^3}$

$\therefore \sqrt[3]{{15625}} = 5 \times 5 = 25$

The cube root of $15625$ is $25.$

vi. $13824$

Ans: Expand $13824$ in factors of prime numbers.

$13824 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3$

$= {2^3} \times {2^3} \times {2^3} \times {3^3}$

Take cube root on both sides of equation.

$\because 13284 = {2^3} \times {2^3} \times {2^3} \times {3^3}$

$\therefore \sqrt[3]{{13284}} = 2 \times 2 \times 2 \times 3 = 24$

The cube root of $13824$ is $24$

vii. $110592$

Ans: Expand $110592$ in factors of prime numbers.

$115092 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3$

$= {2^3} \times {2^3} \times {2^3} \times {2^3} \times {3^3}$

Take cube root on both sides of equation.

$\because 110592 = {2^3} \times {2^3} \times {2^3} \times {2^3} \times {3^3}$

$\therefore \sqrt[3]{{110592}} = 2 \times 2 \times 2 \times 2 \times 3 = 48$

The cube root of $110592$ is $48.$

viii. $46656$

Ans: Expand $46656$ in factors of prime numbers.

$46656 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3$

$= {2^3} \times {2^3} \times {3^3} \times {3^3}$

Take cube root on both sides of equation.

$\because 46656 = {2^3} \times {2^3} \times {3^3} \times {3^3}$

$\therefore \sqrt[3]{{46656}} = 2 \times 2 \times 3 \times 3 = 36$

The cube root of $46656$ is $36.$

ix. $175616$

Ans: Expand $175616$ in factors of prime numbers.

$175616 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 7 \times 7 \times 7$

$= {2^3} \times {2^3} \times {2^3} \times {7^3}$

Take cube root on both sides of equation.

$\because 175616 = {2^3} \times {2^3} \times {2^3} \times {7^3}$

$\therefore \sqrt[3]{{175616}} = 2 \times 2 \times 2 \times 7 = 56$

The cube root of $175616$ is $56.$

x. $91125$

Ans: Expand $91125$ in factors of prime numbers.

$91125 = 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 5 \times 5 \times 5$

$= {3^3} \times {3^3} \times {5^3}$

Take cube root on both sides of equation.

$\because 91125 = {3^3} \times {3^3} \times {5^3}$

$\therefore \sqrt[3]{{91125}} = 3 \times 3 \times 5 = 45$

The cube root of $91125$  is $45.$

2. State true or false.

i) Cube of any odd number is even.

Ans: False. As multiplying an odd number three times will yield an odd number.

For example, the cube of $5$ which is an odd number is $25$, which is also an odd number.

ii) A perfect cube does not end with two zeroes.

Ans: True. Perfect cube will always terminate with multiple of $3$ numbers of zeroes.

For example, the cube of $100$ is $1000000$ and there are $6$ zeros at the end of it.

iii) If square of a number ends with $5$, then its cube ends with $25$.

Ans: False, it is not always certain that if the square of a number ends with $5$, then its cube will end with $25$.

For examples, square of $55$ ends with 5, $3025$ but its cube,$166375$ does not end with $25$.

iv) There is no perfect cube which ends with $8$.

Ans: False, all the numbers having $2$ at its unit digit place will have $8$ in end as cube.

v) The cube of a two digit number may be a three digit number.

Ans: False, as cube of even smallest two digit number, $10$ is a four digit number,$1000$.

vi) The cube of a two digit number may have seven or more digits.

Ans: False, as cube of even largest two digit number, $99$ is a six digit number, $970299$

vii) The cube of a single digit number may be a single digit number.

Ans: True, as a cube of first two natural numbers, $1$ and $2$ are $1$ and $8$ respectively.

## Conclusion

Class 8 Maths Ch 6 Ex 6.2 focuses on cubes and cube roots and calculating cube root, providing essential practice for understanding these concepts. It is important to understand the properties of cubes and cube roots, as well as how to calculate them efficiently. Pay special attention to the methods for finding cubes and cube roots, as these skills are foundational for more advanced mathematical topics. This exercise is crucial for developing strong problem-solving abilities and a deeper understanding of numerical relationships, which will benefit students in their future studies.

## Class 8 Maths Chapter 6: Exercises Breakdown

 Exercise Number of Questions Exercise 6.1 4 Questions & Solutions (4 Short Answer)

## Chapter-Specific NCERT Solutions for Class 8 Maths

Given below are the chapter-wise NCERT Solutions for Class 8 Maths. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.

## FAQs on NCERT Solutions for Class 8 Maths Chapter 6 - Cubes and Cube Roots Exercise 6.2

1. What is the cube of a number in ex 6.2 class 8?

In ex 6.2 class 8, the cube of a number is the result of multiplying the number by itself three times. For example, the cube of 2 is 2×2×2=8. Understanding this concept helps in simplifying and solving complex mathematical problems, making it an essential part of learning cubes and cube roots.

2. Why is understanding cubes and cube roots important in class 8 maths exercise 6.2?

Understanding cubes and cube roots is crucial because they are foundational concepts in mathematics. They assist in solving higher-level algebraic problems and are used in real-life applications, such as calculating volumes. Mastery of these concepts is essential for progressing in mathematics.

3. What properties of cubes should I focus on, in class 8 exercise 6.2?

In class 8 maths 6.2 focus on properties such as the cubes of negative numbers, perfect cubes, and the relationship between a number and its cube root. These properties help in simplifying calculations and solving problems more efficiently, providing a deeper understanding of the concepts.

4. What types of problems are included in class 8 maths ex 6.2 ?

Problems include finding cubes and cube roots, simplifying expressions, and applying properties of cubes. These questions are designed to reinforce theoretical knowledge through practical application, ensuring students grasp the concepts thoroughly.

5. What is the best way to master cubes and cube roots in class 8 maths exercise 6.2 ?

The best way to master cubes and cube roots is to practice regularly, understand the properties and formulas, and apply them to various problems. Consistent practice builds confidence and proficiency, helping students to tackle complex problems with ease.